Single Particle Versus Collectivity, Shapes of Exotic Nuclei

EPJ manuscript No. (will be inserted by the editor)

Single particle versus collectivity, shapes of exotic nuclei

Andrea Jungclaus Instituto de Estructura de la Materia, CSIC, E-28006 Madrid, Spain

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Abstract. In this article some selected topics of nuclear structure research will be discussed as illustration of the progress reached in this ﬁeld during the last thirty years. These examples evidence the improvement of our understanding of the atomic nucleus reached on the basis of countless experiments, performed to study both exotic nuclei (nuclei far-oﬀ the valley of stability) as well as nuclei under exotic conditions (high excitation energy/temperature or large angular momentum/rotational frequency), using stable and radioactive ion beams. The experimental progress, in parallel to the advancement of modern theoretical descriptions, led us to a much richer view of this fundamental many-body system.

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1 Introduction

During the last decades, nuclear structure physics has experienced a worldwide renaissance and our understanding of the atomic nucleus has not only improved, but very often we have found ourselves confronted with real surprises which demanded changes in our view of this fundamental system. As is often the case in the history of science, the very dynamic evolution of this field of research has been closely related to the development of new experimental tools. As we will see in the course of this article, the probably most important new tools were on one hand side the first generation radioactive ion beams and on the other hand highly efficient 4π γ-ray spectrometer in conjunction with different highly sophisticated ancillary detectors. In this article I will not try to provide an all-embracing Fig. 1. Chart of nuclei with the black squares marking the view of nuclear physics research but instead illustrate the about 300 stable nuclei existing in nature. The yellow area accomplished progress by means of some selected topics indicates the region of nuclei which already have been experi- (evidently chosen according to personal taste). The focus mentally studied while the green region consists of thousands of will be on the “simple physics behind” and the qualitative nuclei which are expected to be bound (stable against particle understanding rather then detailed technical or theoreti- emission) but have not yet been produced in terrestrial labora- cal aspects - assuming that many of these are presented tories. Note that many of these nuclei are however continuously in other contributions to this school. produced in the Universe during nucleosynthesis processes. The Fig. 1 shows the chart of nuclides, the orientation map path of the astrophysical rapid neutron capture process is in- for nuclear physicists. The black squares mark the about dicated in blue. Finally, the magic numbers of the nuclear shell 300 stable nuclei existing in nature and forming the valley model are included as black dashed lines. of stability. The nuclei on the left side of this valley decay via β+-decay, the ones on the right hand side via β−-decay. Since the pioneering work by Maria Goeppert-Mayer and excitation spectrum is dominated by single-particle exci- Hans Jensen in 1949 [1], we know that due to the shell tations, whereas nuclei with many protons and neutrons structure of the atomic nucleus, the latter is particularly outside the closed shells are very often deformed. In these stable (has a large binding energy) for certain numbers of nuclei collective excitations such as rotations or vibra- protons and neutrons, the so-called magic numbers. Nu- tions, to which many nucleons contribute, often become clei in the vicinity of closed shells are spherical and their energetically favoured. The basic predictions of both the spherical shell model and the collective models have been Send offprint requests to: confirmed in numerous studies in the past and it seemed 2 Andrea Jungclaus: Single particle versus collectivity, shapes of exotic nuclei that the atomic nucleus is - at least at not too high exci- nuclear physics textbook: i) the half-density radius of the 1/3 tation energy and angular momentum and not too far off matter distribution can be expressed as R = r0A with stability - very well understood. the radius constant r0 = 1.1 − 1.2fm, ii) protons and In the last decades, however, it became possible to ex- neutrons are uniformly mixed in the nucleus, or in other perimentally explore both exotic nuclei as well as nuclei words, there is no large difference observed in radii be- under exotic conditions. By exotic nuclei, we understand tween the proton and neutron distributions and iii) the nuclei far off stability, which includes i) nuclei with large surface thickness is constant. The question we are going isospin (T3=N-Z) close to the driplines and ii) superheavy to discuss now is whether these three common properties nuclei, i.e. nuclei with large mass number (A=N+Z). The of the nuclear density also hold for unstable nuclei. driplines mark the limits of nuclear stability, i.e. outside these borders the nuclei are unstable against the emission Of course, we cannot produce targets of unstable nu- of nucleons. In Section 2 of this article we will discuss how clei to perform scattering experiments with electrons or the first available energetic radioactive ion beams allowed protons. However, in the mid-eighties, first radioactive to study light neutron-rich nuclei and to map the neu- nuclear beams became available allowing for the deter- tron dripline up to Z=11 and what we have learned from mination of matter radii of the unstable nuclei from mea- these studies. After that we move along the neutron-rich sured cross sections for their interaction and reaction with side of the chart of nuclides to slightly heavier systems the nuclei of a stable target. In the pioneering work by and treat the evolution of nuclear shell structure at large Tanihata and co-workers [2], which was performed at the isospin. Then we will discuss recent progress in the study Lawrence Berkeley Laboratory (USA), the interaction cross of the properties of nuclei in the region around doubly- sections between radioactive Li and Be beams and stable magic 132Sn and illustrate the relevance of the new results Be, C, and Al targets have been measured. For the first in view of the astrophysical rapid neutron capture process time, a sudden increase of the square mean radius has (r process) of nucleosynthesis. In Section 3 we move to been observed within the Li chain of isotopes, in partic- the neutron-deficient side of the valley of stability and ular between 9Li and the next bound isotope 11Li. This discuss topics such as the isospin symmetry in medium- observation has been interpreted soon later as first evi- mass N=Z nuclei, the contribution of T =0 isoscalar pair- dence of a neutron halo in 11Li by Hansen and Johnson ing to the properties of heavy N=Z nuclei, the proton [3]. Meanwhile, nuclei radii have been measured for nu- emission in nuclei close to, and in some cases even across, merous light unstable neutron-rich nuclei using the same the proton dripline and finally the phenomenon of shape technique. The results are summarized in a schematic way coexistence. To close the discussion of nuclei close to the in Fig. 2. It is immediately obvious from this figure that 1/3 limits of stability we will discuss in Section 4 the status the R = r0A rule is not valid at all far off stability, of superheavy nucleus synthesis and close with remarks at least in the region of light nuclei. In contrary, large about the spectroscopy of transfermium nuclei. variations in radii are observed. Marked in this figure are Complementary to the investigation of exotic nuclei is the cases of well established 1n and 2n halos and the so the study of nuclei closer to stability, but under exotic far only known case of a proton halo in 8B. Whereas in conditions. In the last section of this article we will try the case of 11Li the radius changes drastically from one to answer questions such as: How does a nucleus behave isotope to the next, a gradual increase of the matter ra- at high angular momentum and/or high excitation ener- dius is observed in the chains of heavier F, Ne and Na gies? Can a collapse of pairing correlations be observed isotopes. This phenomenon is understood as a neutron under these circumstances? How does the shape of a nu- skin, which is an excess of neutrons at the nuclear sur- cleus change with angular momentum? What is the limit face. Generally it is not trivial to determine the radii of of deformation a nucleus can sustain? Finally, the arti- the proton and neutron distributions separately. An esti- cle closes with a short outlook on the future of nuclear mate of the charge radius can be obtained from the cross structure research. sections for charge-changing reactions at relativistic energies. However, a unique opportunity for a precise comparison between matter and charge radii over a wide range 2 The neutron-rich side of the nuclear chart of neutron numbers is offered by the Na isotopes, since their rms charge radii have been determined in isotope- 2.1 Halos, skins and clusters in light nuclei shift measurements [4]. The matter radii were determined as described above [5] and the resulting proton and neu- The nuclear size and the proton and neutron density dis- tron radii are shown in Fig. 2. We can see a gradual growth tributions are important bulk properties of nuclei that de- of the thickness of the neutron skin for neutron-rich Na termine the nuclear potential, single-particle orbitals, and isotopes up to 0.4 fm. It should be mentioned that addi- wave functions. Historically, the proton or charge distri- tional information about the halo structure of neutron-rich butions of stable nuclei have been studied using electron nuclei, e.g. the wave function and density distribution of scattering, whereas for the measurement of the matter dis- the valence nucleons, can be obtained from the measure- tributions strong interacting probes have to be used and ment of the momentum distribution of fragments after elastic proton scattering provides the best information. their break-up (see also Section 2.3) or the cross sections From these studies, three basic properties have been es- for Coulomb break-up reactions. Narrow momentum dis- tablished and can be found on the first pages of every tributions of fragments as well as large Coulomb break-up Andrea Jungclaus: Single particle versus collectivity, shapes of exotic nuclei 3

1n Halo Mg d d Borromean Na d ´core´+4n Ne F 1p Halo O 8 N 20 C 3.5 n B Na Be Li Li 3.0 He 2 p H [fm] radio 2.5 8 8 12 16 20 2 A N

Fig. 2. Schematic summary of experimental quadratic mean square radii. The six different circle sizes correspond to the range of 2.0-3.5 fm. The experimental driplines are shown in red (neutrons) and blue (protons). In the lower part the mean square quadratic radii of the Li and Na isotopes (in the latter case separately for protons and neutrons) are shown while on the right hand side of the figure the sizes of some selected nuclei are illustrated. probabilities indicate a relatively large spatial extent of Nitrogen and Oxygen isotopes are 23N and 24O with the the valence nucleon(s) [6,7]. A very nice review of the ex- same neutron number, N=16, while the heaviest isotope perimental status of nuclear halo structure studies is given of fluorine observed so far is 31F with N=22. It is very in Ref. [8]. astonishing that six additional neutrons can be bound by moving from Oxygen to Fluorine by adding just one proton. This location of the dripline for O and F is hardly predicted by mass formulas, most of which favor 26O and 29F as heaviest isotopes. Fig. 3 shows that above Z=9, the 2.2 Mapping of the neutron dripline dripline follows a more regular path as expected from mass formulas. The next N=2Z+4 isotopes behind 31F, namely The existence of a given nucleus is one of the most basic 34 37 questions nuclear physics must answer. Therefore, aside Ne and Na, are bound, too. Our current knowledge of from the study of the matter and charge distributions of the neutron dripline is limited to Z≤11 and one of the neutron-rich light nuclei, already the mapping of the neu- major goals for the future is to extent it to the heavier region. A first step in this direction constitutes the dis- tron dripline by itself is of major importance. One reason 40 42 is that it allows to prove different mass predictions, an- covery of Mg and Al which was recently presented by other that shell effects should influence the nuclear bind- Baumann et al. [11]. ing and therefore the exact position of the dripline. Many Let us come back now to the unexpected position of experiments performed to map the dripline are very simi- the dripline for the O and F nuclei. The sudden change in lar to the ones described in the last section. The neutron- stability from oxygen to fluorine indicates an extra push of rich nuclei are produced in projectile fragmentation and stability for the very neutron-rich fluorine isotopes. Where identified using fragment recoil separators. As example, might this extra stability come from? One hint is given by the particle identification plots obtained using the RIPS the fact that among all the mass formulas on the market spectrometer at RIKEN (Tokyo, Japan) and the fragmen- only the finite-range droplet model predicts the stability tation of a) a 94.1 MeV/u 40Ar beam and b) a 48Ca beam of 31F (and also 31Ne). This model includes nuclear defor- at 64 MeV/u are shown in Fig. 3 [9,10]. From this figure, it mation effects so one possible origin of the anomaly could is immediately evident that the N=2Z+4 nucleus 31F ex- be related to ground state deformation. Both 31Ne and ists, whereas no events corresponding to 28O and 25N have 31F with N=21 and N=22 are quite close to the N=20 been observed. In the same way, the N=2Z+2 isotope 26O shell closure of the spherical shell model. So one may ask has not been detected though the heavier N=2Z+2 nuclei whether the magic number N=20, implying closed shells 29F and 32Ne could clearly be identified. Note, that none and sphericity for nuclei close to the valley of stability, is of the N=2Z+3 nuclei in the range 5≤Z≤10 has been still magic far off stability. This brings us directly to our observed. The current knowledge of the neutron dripline next topic. obtained from this kind of experiments is summarized in Fig. 3. The most puzzling observation is that the heaviest Neutron dripline anomaly around flourine 4 Andrea Jungclaus: Single particle versus collectivity, shapes of exotic nuclei

Fragmentation of 40Ar @ 94.1 MeV/u Fragmentation of 48Ca @ 64 MeV/u

Z Z N=2Z+2 14 N=2Z N=2Z+2 32 N=2Z+4 10 Ne 31 N=2Z+4 29F F 0.15(06) pb 12 Z Mg 37Na 26O 28O Na 8 34Ne Ne 23N 25N 10 31F F 20 2237 6 C C Na Neutron dripline anomaly around flourine O N=2Z+2 8 19 8 17B B N 20 Fragmentati3.0 on of 403.2Ar @ 94.13.4 MeV/u Fragmentation of 48Ca @ 64 MeV/u 34 A/Z C 3.2 3.4 31 3.6 3.8Ne 24 A/ZF Z B O H. ZSakurai et al., Physics Letters B448 (1999) 180 Be both experiments performed M. Notani et al.,N=2Z+2 Physics Letters B542 (2002) 49 14 N=2Z N=2Z+2 at RIKEN (Japan) 32 N=2Z+4 10 Ne Li N=2Z+4 29 31F He 2 F 0.15(06) pb 12 37Na 26O 28O H 8 8 N=2Z+4 34Ne 2 23N 25N 10 N 31F 20 22 6 C C 19 8 17B B 3.0 3.2 3.4 3.2 3.4 3.6 3.8 A/Z A/Z H. Sakurai et al., Physics Letters B448 (1999) 180 both experiments performed M. Notani et al., Physics Letters B542 (2002) 49 Fig. 3. Experimental neutron dripline in light nuclei up to Na illustrating the anomaly in itsat RIKEN path (Japan) for oxigen and fluorine isotopes. The insets show particle identification plots (Z vs. A/Z) obtained in two experiments performed at RIKEN employing the fragmentation of 40Ar and 48Ca beams [9,10]. In these plots each blob corresponds to a different isotope. A non-observation of a certain isotope implies that it is unbound (if it is not simply due to a lack of statistics).

2.3 Shell evolution close to the neutron dripline figurations lead to the denomination island of inversion for the region around N=20, in which the deformed 2p-2h In this article we will only present a short summary of configuration forms the ground state. In the last decades the historic developments and the present status of our numerous experiments, dedicated to the measurement of knowledge with respect to the evolution of the nuclear quantities such as electromagnetic transition strength and shell structure in the regions far-off the valley of stability. moments and employing a number of different reactions A more detailed discussion is not only outside the scope using slow and fast radioactive ion beams, allowed to de- of the present article but also dispensable considering the termine the extent of the island of inversion, which is large number of review articles covering this topic. Quite schematically indicated in Fig. 4, and construct a detailed general information can be found in Refs. [12–15]. and consistent picture of the structural changes taking One of the first experimental indications for changes place in this region of the nuclear chart. in the shell structure in neutron-rich nuclei dates back to 1975 when the masses of the Na isotopes were measured by Thibault et al. at ISOLDE (CERN, Switzerland) [16]. The results showed that the N=20,21 isotopes 31,32Na “are monopole effects of the more tightly bound than expected from theoretical pre- tensor force Cr + 32 f V dictions”. Four years later, the first 2 state in Mg 7/2 20 Ti 54Ca was populated for the first time in the β decay of 32Na Sc l+1/2 l-1/2 Ca [17]. Its low excitation energy of 0.885 MeV, more than d K N=40 3/2 Ar 2.4 MeV lower as compared to the corresponding ener- Cl 34 36 s S gies in the heavier N=20 isotones Si and S, clearly 1/2 P Si N=34 demonstrated a change of structure along the N=20 iso- Al Mg tonic chain towards the neutron dripline. On the theoreti- d5/2 Na N=28 Ne 24 cal side, the first explanation for the experimental findings F O ? was presented by Warburton et al. within the framework O p1/2 N N=20 of the nuclear shell model [18]. In that work it was sug- C gested that in 32Mg and some other nearby nuclei the de- N=8 N=16 formed two-particle-two-hole (2p-2h) configuration, com- d5/2 s1/2 d3/2 f7/2 p3/2 p1/2 f5/2 prising the excitation of a neutron pair across the N=20 shell gap, would become energetically favoured and thus Fig. 4. Part of the chart of nuclides illustrating the shell evo- form the ground state. This inversion in excitation energy lution on the neutron-rich side close to the neutron dripline between the spherical 0p-0h and the deformed 2p-2h con- (see text for details). Andrea Jungclaus: Single particle versus collectivity, shapes of exotic nuclei 5

Later, the Monte Carlo shell model studies of the Tokyo group revealed the importance of the T =0 monopole in- 11Li teraction between the protons and neutrons for the description of the experimental findings [19,20]. This inter- 24O action is strongly attractive between orbital pairs with p1/2 s j=l+1/2 and j=l-1/2 while it is repulsive whenever the 1/2 two nucleons both populate orbitals with either j=l+1/2 or j=l-1/2. These so-called monopole effects of the tensor force are responsible not only for the shell evolution d s1/2 3/2 around N=20 but also in other regions of the nuclear chart as we will see later. In the case of the island of inversion, the removal of protons from the d5/2 orbital when moving 34 28 from Si down along the N=20 line towards O pushes 2p1/2 2p1/2 2p 1f5/2 2p 1f5/2 the neutron d3/2 orbital up in energy (less proton-neutron 28 3/2 28 3/2 1f 1f pairs in the j=l±1/2 orbitals d3/2 and d5/2). When the 7/2 7/2 20 1d3/2 1d3/2 d3/2 approaches the f7/2 orbit above, the N=20 gap disap- 2s 1/2 16 pears and a new gap opens between s1/2 and d3/2, i.e. for 1d5/2 24 N=16. Consequently, in this picture O is expected to be 2s1/2 8 1d a new doubly-magic nucleus. Experimentally, the magic- 5/2 1p1/2 1p1/2 ity of this nucleus was demonstrated by Kanungo et al. in 1p3/2 1p3/2 2009 by measuring the longitudinal momentum distribution of one-neutron removal from 24O [21]. The measured 2 2 momentum distribution is very well described assuming 1s1/2 1s1/2 that the last neutron occupies the s1/2 orbital, no contribution from the d3/2 orbit is observed. This finding clearly Fig. 5. Top: Measured longitudinal momentum distributions indicates the existence of an energy gap between these two of one-neutron removal from 11Li and 24O. The data are daten orbitals, i.e. at N=16. Note that this scenario is in con- from Refs. [22,21]. The bottom panel illustrates the conse- trast to the one observed for 11Li ten years before. In that quences of the measured momentum distributions for the evo- case, Simon et al. found that the measured momentum dis- lution of shell structure. tribution can only be described assuming a roughly equal occupancy of the p1/2 and s1/2 neutron orbitals [22]. This has been at that time the first indication of a vanishing different orbitals depends on a variety of different subtle N=8 shell gap away from stability, since the existence of a effects, not only the monopole term of the tensor force. significant gap would prevent the neutron from occupying Whether the size of the N=34 gap is really large enough the s orbital above the shell closure (see Fig. 5). to call N=34 a new magic number is in my opinion not so 1/2 clear. In another Nature article [24], published just four Inspection of Fig. 4 shows that the neutron-rich Ca iso- months before Ref. [23], mass measurements were pre- topes offer an ideal opportunity to test the validity of the sented which “unambiguously establish a prominent shell picture discussed above, namely the idea that monopole closure at neutron number N=32”. Note, that N=32 and effects of the tensor force are responsible for the disappear- N=34 are only separated by the p1/2 orbital! ance of the N=20 magic number in the island of inver- So far we discussed the evolution solely within the sion and the opening of a new shell gap at N=16. While framework of the nuclear shell model and tried to un- the attractive interaction between protons and neutrons derstand the experimental observation using simple pic- in the spin-orbit partner orbitals d3/2 and d5/2 played a tures. We would like to mention, however, that besides major role there, the same picture should apply to the the SM there is a second main theoretical approach to next spin-orbit pair, namely the f5/2 and f7/2 orbitals. study the structure of the atomic nucleus, namely the The removal of protons from the f7/2 orbit when going mean field theory and beyond. The basic mean field ap- from stable 62Ni down to 54Ca should then reduce the proach is the Hartree-Fock-Bogolibov (HFB) in which the binding of the f5/2 proton orbital, therefore increase its long range part of the nuclear interaction (particle-hole) energy and consequently lead to the development of a sub- and the short range part (particle-particle) are treated at shell gap for N=34 (compare Fig. 4). The trueness of this the same foot and allows a good description of deforma- prediction has recently been investigated experimentally tions and pairing properties. As a matter of fact the HFB using in-beam γ-ray spectroscopy and proton knock-out approach, in conjunction with density dependent interac- reactions at relativistic energies at RIKEN [23]. In that tions like Skyrme and Gogny, is well known since long ago work the excitation energy of the first excited 2+ state in for providing a good description of nuclear bulk properties 54Ca was measured and, in comparison to state-of-the-art like binding energies, quadrupole moments, pairing gaps, shell model calculations, interpreted as “direct experimen- radii etc, all over the periodic table. The Gogny force in tal evidence for the onset of a sizable sub-shell closure at particular has a large predicting power. Recently there has neutron number 34 in isotopes far from stability”. Note, been two main advances in the mean field approaches [25]. however, that the evolution of the relative positions of the First, by the recovery of the symmetries, like the particle 6 Andrea Jungclaus: Single particle versus collectivity, shapes of exotic nuclei number and the angular momentum broken in the HFB cay into the stable or semistable isotopes observed in the approach, by the projection technique. And second, by solar system. However, none of the proposed stellar sce- including fluctuations, around the most probable values narios, including the explosion of supernovae and merging of the HFB theory, by the Generator Coordinate method neutron stars, can fully explain the available abundance (GCM) like the (β, γ) deformations [26], the pairing gaps observations. Also the mechanism of the r process is un- (∆Z , ∆N ) [27] and very recently the angular frequency certain. Nuclear physics properties such as β-decay half- (¯hω) [28]. The combination of these two developments in lives and masses are key for predicting abundance pat- the so called Symmetry Conserving Configuration Mix- terns and thus extracting signatures of the r process from ing Approach (SCCMA) provides the description of nu- a detailed comparison to astronomical observations. The clear spectroscopic properties with a high accuracy. Fur- nuclei below doubly-magic 132Sn, i.e. the ones with pro- thermore the use of a single interaction along the nuclide ton number Z≤50 and neutron number N∼82, are cru- chart with a good description of bulk properties, provides cial in any r-process mechanism because their enhanced a large predicting power to these approaches. The exam- binding bends the r-process path closer to stability (com- ples of shell evolution discussed above are discussed in the pare Fig. 1) slowing down the reaction flow. The half-lives framework of beyond mean field theory in Refs. [28–30]. of these so-called waiting-point nuclei determine the time Moving from the disappearance of the N=20 magic scale of the r process and shape the prominent r-process number and the simultaneous emergence of a shell gap at abundance peak of isotopes with A∼130. The precise theo- N=16 to the case of a potential new N=34 sub-shell clo- retical prediction of these half-lives is challenging because sure, we skipped the discussion of a possible alteration of the structure evolution of neutron-rich N∼82 nuclei is still the N=28 magic number. This is the first of the classi- unknown. cal magic numbers which originates from the spin-orbit In a recent experiment performed at the RIBF facility interaction. Although in contrast to the case of N=20 at RIKEN the half-lives of 110 neutron-rich nuclei across the dripline has not yet been reached experimentally for the N=82 shell gap were measured, 40 of them for the N=28, numerous experiments have evidenced modifica- first time [34]. The implications of these new half-lives for tions of this shell gap in the very neutron-rich isotope 42Si the r process were investigated by conducting a fully dy- [31–33]. The results pinpoint the effects of several terms of namic reaction-network calculation study that simulated a the nucleon-nucleon interaction, besides the already dis- spherically symmetric outflow from a neutron-rich stellar cussed tensor component, namely the central, the spin- environment. The impact of the new measurements on the orbit and the three-body contributions. All these aspects calculated solar-abundance pattern is illustrated in Fig. 6, are discussed in detail in Ref. [15] so that it is not neces- where two calculations are compared that differ only by sary nor beneficial to repeat it here. For the larger magic the use of the newly measured half-lives instead of theo- numbers, namely 50, 82 and 126, the neutron dripline is retical values. All the other nuclear structure data, as well still far out of reach experimentally and theoretical calcu- as the astrophysics conditions, were the same. The new lations predicting changes in the shell structure of heavy half-lives have a global impact on the calculated r-process neutron-rich nuclei are therefore difficult to test. In par- abundances, and alleviate the underproduction of isotopes ticular, the evolution of the N=82 shell gap has been sub- just below and above the A∼130 peak, which in the past ject of numerous theoretical studies in the past since it required the introduction of shell-structure modifications is of utmost importance for the exact course of the as- [35,36]. A particularly beneficial effect of the new half-lives trophysical rapid neutron capture process (r process) of of the most neutron-rich isotopes of Ag, Cd, In, and Sn nucleosynthesis. To which extent experimental informa- (N>82), is to greatly improve the description of the abun- tion can contribute to the better understanding of such dance of rare earth elements, which is a prerequisite for fundamental processes even without reaching the limits of studying the universality of the r process. The reduced nuclear binding, i.e. the dripline, will be discussed in the nuclear physics uncertainty provides a new level of reli- next section. ability for r-process calculations and their parametrized astrophysical conditions.

2.4 The region around doubly-magic 132Sn and the r process of nucleosynthesis 3 The neutron-deﬁcient side of the nuclear The origin of the heavy elements from iron to uranium chart is one of the main open questions in science. The slow neutron-capture process (s process) of nucleosynthesis, oc- While we have shown in Section 2 that most of the progress curring primarily in helium-burning zones of stars, pro- achieved during the last decades on the neutron-rich side duces about half of the heavy element abundance in the of the nuclear chart is owing to the availability of low- Universe. The remaining half requires a more violent pro- and high-energy radioactive ion beams, on the neutron- cess, the r process. During the r process, in environments deﬁcient side the majority of nuclei up to the proton dripline of extreme temperatures and neutron densities, a reaction can be studied using stable ion beams employing the fusion- network of neutron captures and β decays synthesizes very evaporation reaction, which is also called compound nu- neutron-rich isotopes in a fraction of a second. These iso- cleus reaction. In this reaction two stable nuclei are brought topes, upon exhaustion of the supply of free neutrons, de- together at an energy above the Coulomb barrier. The Andrea Jungclaus: Single particle versus collectivity, shapes of exotic nuclei 7

without new half-lives

with new half-lives

Fig. 6. Left: Particle identification plot showing all events according to the reconstructued values of the atomic mass, Z, and the mass-to-charge ratio, A/q. Nuclei with newly measured half-lives are on the right side of the red solid line. The heaviest masses for which half-lives could be measured are highlighted by red circles. Right: Comparison between the r-process solar abundance pattern and the abundances calculated without (top) and with (bottom) the new experimental half-lives. Figure adopted from Ref. [34]. formed system then either fissions immediately or a com- the atomic nucleus under extreme conditions of excitation pound nucleus is formed in a highly excited state as illus- energy and rotational frequency. Phenomena which only trated in Fig. 7. The compound nucleus reaches statisti- arise under these conditions will be discussed in Section cal equilibrium and subsequently decays mainly by parti- 5. cle emission until this is no longer possible energetically. Alternatively, with a branching of 10−2-10−4, the disexci- tation also proceeds by high-energy γ rays from the giant 3.1 Proton emitters and proton radioactivity dipole resonance. Finally, the residual nuclei deexcite to the ground state via the emission of γ radiation. In the time interval between the formation and the decay of the The limits of stability, i.e. the driplines, are reached when compound nucleus, the excitation energy is shared statis- the nuclear force is no longer able to bind an ensemble of nucleons with a too large neutron or proton excess. tically among its constituent nucleons so that all memory 14 of its mode of formation is lost. The processes of forma- Whereas for heavy nuclei, α decay, C radioactivity or tion and decay are thus independent of each other. This fission occurs, unstable proton-rich (or neutron-deficient) reaction produces nuclei on the neutron-deficient side of nuclei may decay from their ground states by the emis- the valley of stability because stable light or medium mass sion of one proton in the case of odd-Z nuclei or of two nuclei used as target and/or projectile have a lower N/Z protons for even-Z nuclei. The one-proton ground state ratio as compared to heavy stable nuclei (see Fig. 1). Us- decay was observed for the first time at GSI (Darmstadt, ing this reaction a variety of physics topics has been stud- Germany) in 1981 [37,38]. In the meantime, more than 30 ied in neutron-deficient nuclei in the past, for example cases of proton radioactivity have been identified for odd- the proton emission from ground and excited states, the Z nuclei beyond the proton drip line between Z=51 and isospin symmetry in N=Z nuclei or the shape existence Z=83. This decay mode so far has only been observed phenomenon. These topics will be discussed in the follow- for relatively heavy nuclei because here the presence of ing subsections. Furthermore, the fusion-evaporation re- a large Coulomb barrier reduces the proton barrier pen- action is also the main tool to study the heavy end of the etration probability to the extent that proton decays of nuclear chart, i.e. to synthesize superheavy elements or to nuclei from their ground state have measurably long half- perform spectroscopy of transfermium nuclei (see Section lives. The proton decay rate depends both on the energy 4). Finally, since this reaction allows to populate highly and orbital angular momentum of the emitted proton as excited states with high angular momentum (see Fig. 7), well as on the wave function of the proton-decaying state, it is also perfectly suited, in combination with highly- which is determined by the shape of the nuclear poten- efficient γ-ray spectrometer, to investigate the behavior of tial and by residual interactions between valence nucleons. The measurement of proton decay rates is therefore a 8 Andrea Jungclaus: Single particle versus collectivity, shapes of exotic nuclei

Using this technique, it has been possible to observe rota-

target nucleus tional bands feeding both the ground state (T1/2=4.2(4) ms) and a second proton-emitting state, namely an isomer fission at about 60 keV excitation energy (T1/2=8(3) µs) [39]. 141 -22 This observation constitutes direct evidence that Ho is projectile fusion 10 sec formation of a 3-5 MeV/u deformed. A quadrupole deformation of β = 0.25(4) was Compound nucleus 2 deduced for the ground state from the extracted dynamic

Ex [MeV] moment of inertia. In a later study [40], a fine structure 20 ħω ~ 0.75 MeV ~ 2x1020 Hz in the proton emission from both states was observed, in- + 140 rotation dicating the population of the first 2 state in Dy with I 15 after particle a branching ratio of 1-2%, competing with the dominant p + evaporation p branch to the 0 ground state. statistical dipole cascades -19 p 10 10 sec n Already in 1960 two-proton radioactivity has been predicted to occur for even-Z proton-rich nuclei beyond the I Yrast line dripline [41]. This process is very difficult to observe and 5 discrete γ-transitions only in 2002, two-proton radioactivity has been observed 45 no states 10-15 sec for the first time in Fe [42,43], see below. However, al- γ 0 ready in 1983 the first case of β-delayed 2p emission was 0 5 10 15 20 25 Spin I [h] discovered [44] and up to now, several other cases are 10-9 sec established. Beta-delayed multiparticle emission becomes

ground state increasingly important when approaching the drip lines because the Qβ values increase while the particle sepa- Fig. 7. Schematical illustration of the compound nucleus re- ration energies decrease [45]. In nearly all cases, the ob- action. The inset shows the population of excited states of the served β2p originates from the Isobaric Analogue State in reaction products in the excitation energy vs. spin plane. the daughter nucleus. It these studies, it has been possible to answer the question about the underlying decay mechanism. In principle, both a direct emission of two protons as well as a sequential decay via intermediate states is unique tool to establish the sequence of shell-model single- possible. Whereas in the latter case, the individual pro- particle levels beyond the proton drip line. Whereas most ton energies depend on the intermediate state and the of the known proton emitters have decay rates consistent proton energy spectrum therefore exhibits peaks at cer- with the assumption of a spherical potential, for some tain energies, this spectrum is continuous in direct emis- proton emitters in the rare earth region anomalous decay sion. A second criterion comes from the angular distribu- rates were observed indicating the onset of deformation. A tion between the two protons. Whereas in the sequential more direct way to deduce information about the shape of case the angular dependence introduced by the momen- a nucleus is of course the determination of its excitation tum coupling is negligible, the angular distribution is far spectrum. However, proton emitters are populated only from being isotropic in direct emission. Using these two with very small cross sections in heavy-ion induced fusion- criteria, it has been shown that in all known cases of beta- evaporation reactions with stable ion beams, ranging from delayed two-proton emission the mechanism is sequential hundreds of microbarns to tens of nanobarns. Further- decay and it is therefore possible to derive information more, these rare events have to be identified in the pres- about excited states in the intermediate nucleus. No ev- ence of a background of hundreds of millibarns from the idence of a non-sequential decay could be pointed out. strong reaction channels. Therefore prompt γ-ray spec- However, if there is no accessible intermediate state, the troscopy of proton emitters beyond the drip line became sequential emission is forbidden and the emission of the feasible only very recently employing the recoil-decay tag- two protons is simultaneous. This situation is expected for ging method in combination with highly-efficient 4π γ-ray ground state decays of some even-Z nuclei, which due to spectrometer (see Section 5). As one recent example, we the pairing energy are more bound than the one-proton will discuss the γ-spectroscopic study of the proton emit- daughter. Then two cases can be distinguished: First, the ter 141Ho. This nucleus has been populated in the fusion- decay may proceed via a three-body disintegration. This evaporation reaction 92Mo(54Fe,p4n) with a cross section has been observed for the two-proton decays of the broad of about 100 nb [39], which has to be compared to the total resonance states of 6Be [46] and 12O [47]. Secondly, the reaction cross section in the order of 1 b. That means that nuclear state may decay via 2He emission and a strong only in one out of 10,000,000 reactions between target and angular and energy correlation between the two resulting beam nuclei, 141Ho is the reaction product. The trick of protons may be expected. The nucleus 45Fe has been the the recoil decay tagging technique is to correlate evapora- first case for which two-proton radioactivity from a nar- tion residues, which are unambiguously identified by their row nuclear ground state was observed in 2002, namely in subsequent decay which takes place several µs or even mil- two experiments performed at the same time at GSI [42] liseconds after their production, with prompt γ-rays, de- and GANIL [43]. In both cases projectile fragmentation of tected immediately after the nuclear reaction took place. a 58Ni beam was used to produce 45Fe, at 650 MeV/u at Andrea Jungclaus: Single particle versus collectivity, shapes of exotic nuclei 9

GSI and at a lower energy of 75 MeV/u at GANIL. The fragments were identified on the basis of flight times and energy losses and then stopped in position sensitive silicon detectors which allowed to observe their subsequent decays. The two-proton decay mode was unambiguously identified by measuring the decay energy and half-life and the observation of the daughter decay with a half-life in agreement with the half-life of 43Cr, the 2p daughter of 45Fe, and in disagreement with all other possible daughters (for details see [42,43]). Note that in these experiments as few as 5 and 20 decay events of 45Fe were detected at GSI and GANIL, respectively. After these pioneering experiments, several other cases of two-proton radioactivity were observed. However, in none of these experiments, the two protons were identified separately. A real break- through was then achieved five years later, again nearly at the same time independently by two different research collaborations, employing a very powerful new technique. Instead of implanting the 45Fe ions produced in fragmentation reaction in position sensitive silicon detectors, they were now implanted in time-projection chambers (TPC), which allow for a visualization in three dimensions of implantation and decay events and consequently for a direct observation of the individual protons. In an experiment performed at GANIL (Caen, France) a total of 10 45Fe were implanted in a TPC and correlated with successive decays [48]. At NSCL (MSU, USA) even 125 decays were observed, 87 of them followed by 2p emission and 38 by β decay with successive proton emission [49]. In this experiment the 45Fe ions were implanted in an optical TPC which allows to take photographs of the 2p decays. An example of such an image recorded by a CCD camera is shown in Fig. 8. A track of a 45Fe ion entering the cham- Fig. 8. Top: Image of a two-proton decay of 45Fe registered by ber from the left is seen. The two bright, short tracks are a CCD camera. The long track corresponds to the ion entering protons of approximately 0.6 MeV, emitted 535 µs after the TPC from the left while the two short tracks are the two the implantation. This single image is the most impressive protons emitted in the ground-state decay. Bottom: Measured proof for the existence of ground-state two-proton radioac- distribution of the opening angle between the two protons emit- 45 tivity as nuclear decay mode. The information from the ted in the decay of Fe (histogram) compared to predictions optical TPC allows for a full reconstruction of the decay of a three-body model. Figure adopted from Ref. [49]. event in three dimensions. It is therefore possible to determine the opening angle between the two protons emitted in the decay of 45Fe. The distribution of this opening angle 3.2 Isospin symmetry studies in N=Z nuclei is a clear signature for the decay mechanism, three-body disintegration versus 2He emission (see above). The mea- The nuclei on, and around, the line of N=Z between A∼40 sured distribution of this opening angle is shown in Fig. 8. and A∼70 have been the focus of enormous experimental A two-bumped structure is evident with one broad peak effort in recent years. In this region, a rapid evolution of around 50◦ and a smaller one around 145◦. It is nicely structure occurs when leaving the line of stability towards reproduced by predictions of a model which includes ex- the proton dripline. This is also a region where state-of- plicitly the three-body dynamics of the decay process. On the-art shell-model calculations are available which can the other hand, a simple diproton scenario can be ruled help to interpret experimental data. One of the most im- out since in this case, a distribution containing only one portant aspects is that these nuclei allow to study one of narrow peak around 30◦ is expected, in clear contradiction the fundamental symmetries of modern physics, namely to the experimental finding. the neutron-proton exchange symmetry that leads to the concept of isospin in nuclear physics. Isospin symmetry is a consequence of the almost perfect charge-independence and charge symmetry of the attractive strong nucleonnucleon interaction. The symmetry is most evident when A summary of the very impressive progress achieved considering reflections along the N=Z line, i.e. studying in recent years in the study of radioactive decays at the nuclei with exchanged numbers of neutrons and protons, limits of nuclear stability is presented in Ref. [50]. the so-called mirror nuclei. As a case study we will discuss 10 Andrea Jungclaus: Single particle versus collectivity, shapes of exotic nuclei

non-Coulomb isospin-breaking term of isovector origin (for details see Ref. [51]). The result of this comparison is that T=1, S=0 triplet this nuclear isospin-breaking (NIB) component, although a factor two to three smaller as compared to the Coulomb term, is indeed important and needs to be taken into con- singlet T=0, S=1 sideration. Another approach probing isospin mixing at finite temperature is the study of the giant dipole reso- nn np pp nance in N=Z nuclei (see Ref. [53]). A detailed discussion of Coulomb energy differences in isobaric multiplets and T : +1 0 -1 Z their interpretation is presented in the review article by Bentley and Lenzi [54]. NIB 3.3 The isoscalar T =0 pairing phase exp. TED Coulomb In the last section we discussed the isospin symmetry, and the effects which break this symmetry, comparing the en- calc. TED = Coulomb + NIB ergies of excited T =1 states in an isobaric triplet, i.e. the three isobars with Tz=+1, 0, and -1. Isospin T =1 pairing is dominant at low excitation energies for all known nuclei up to around mass 80, including those residing along the N=Z line. In these nuclei, proton-proton pairs and neutron-neutron pairs dominate providing properties sim- Fig. 9. Upper part: Illustration of the two different types of ilar to superfluid helium and superconducting solids. How- proton-neutron pairing, T =0 and T =1. Note that T =0 pair- ever, there are long-standing theoretical predictions that ing is forbidden for proton-proton and neutron-neutron pairs. this situation may change, from a nuclear superfluid dom- Lower part: Experimental triplet energy difference, TED, as inated by isovector pairing to a structure where isoscalar, a function of spin for the A=54 isobaric triplet. The experi- i.e. T =0, proton-neutron pairing plays a major role, for mental values (black triangles) are compared to the result of heavier nuclei towards the exotic doubly-magic nucleus shell model calculations including both Coulomb and nuclear 100Sn, the heaviest N=Z nucleus predicted to be bound. isospin-breaking (NIB) terms. Heavy N=Z nuclei with mass A>90 are difficult to study since they can only be produced, again employing fusion- evaporation reactions, with very low cross-section and in the example of the mirror pair 54Ni/54Fe with 28/26 pro- the presence of background from other reaction channels tons and 26/58 neutrons, respectively. These two nuclei which is many orders of magnitude stronger. The heaviest have Tz=-1,+1, respectively, and the ground state struc- self-conjugate nucleus, for which excited states have been ture of each nucleus has isospin T =1 (see Fig. 9). The observed so far, is 92Pd. It has been produced as two- sets of T =1 states in these two nuclei would be identi- neutron evaporation reaction channel of the compound cal for a perfectly charge-symmetric nuclear force and in nucleus reaction 58Ni(36Ar,2n) at GANIL [55] with a rela- the absence of any other isospin-breaking effects. How- tive yield of less than 10−5 of the total fusion cross-section. ever, one obvious and unavoidable effect which breaks Light charged particles and neutrons were detected in co- the isospin symmetry is of course the Coulomb force be- incidence with the emitted γ radiation to allow for channel tween protons. But is this the only one? To investigate selection. In this experiment three γ rays were assigned this question for the A=54 mirror pair, the most diffi- to the decay of excited states of 92Pd and arranged in cult part is the identification of excited states in the ex- a ground-state band based on their relative intensities. otic N=Z - 2 nucleus 54Ni. Two different experimental The excitation energies of the first (2+), (4+), and (6+) approaches have been successfully employed to study this states were then compared to the results of shell model nucleus: The fusion-evaporation reaction 28Si(28Si,2n)54Ni calculations as shown in Fig. 10. Both the experimental and the EUROBALL γ-ray spectrometer coupled to neu- and the calculated spectra of 92Pd, with four proton holes tron detectors at the IReS Strasbourg (France) [51] and and four neutron holes relative to the 100Sn core, exhibit a the fragmentation of a 58Ni beam at relativistic energies nearly constant energy spacing between consecutive levels. at GSI (Darmstadt, Germany) [52]. In these experiments This is in clear contrast to the seniority coupling scheme the excitation energies of the first J π = 2+, 4+, 6+, 8+, which dominates for nuclei in the normal isovector pair- and 10+ states were measured allowing now for a com- ing phase, for example the N=50 isotone 96Pd with four parison to the less exotic mirror nucleus 54Fe. The quan- proton holes relative to 100Sn. In the latter case, the tran- 54 54 54 + tity TED(J) = EJ ( Ni) + EJ ( Fe) - 2EJ ( Co), the so- sition from the ground state to the first excited 2 state called triplet energy difference, as function of the spin is requires the breaking of one g9/2 proton-hole pair, and shown in the lower part of Fig. 9. It is compared to mod- therefore the energy spacing between these two levels is ern shell model calculations which consider both the well- rather large. The distance between the subsequent levels understood Coulomb contribution as well as an additional then gradually decreases as the angular momentum vec- Andrea Jungclaus: Single particle versus collectivity, shapes of exotic nuclei 11

(constrained by identical chemical bonds). Atomic nuclei do not possess a substructure with widely spaced subunits. The phenomenon of shape coexistence is observed all over the nuclear chart, from the cluster structures observed in light nuclei towards the fission isomers in heavy systems. One prominent example of coexisting spherical and deformed states has been discussed in Section 2.3. There it was reported that the N=20 shell closure disappears moving towards the neutron dripline because in 32Mg the deformed two-particle-two-hole configuration (2p-2h), which comprises the excitation of a neutron pair across the N=20 shell gap, becomes energetically favoured as compared to the normal, spherical 0p-0h configuration. Another man- ifestation of shape coexistence, namely the occurrence of superdeformed bands in nuclei which are spherical in their ground state, will be discussed later in Section 5.1. Here we will briefly mention a very special case of shape coexistence, namely the triple shape coexistence discovered in the heavy neutron-deficient nucleus 186Pb [56]. Excited Fig. 10. Left: Comparison between experimental excitation states in this nucleus have been populated in the α de- 190 energies in the ground-state band of 92Pd and the results cay of Po which in turn was produced in the fusion- 142 52 190 of different shell model calculations. Shell model calculations evaporation reaction Nd( Cr,4n) Po at GSI. At this were performed including either the full proton-neutron pair- point, it is worth mentioning again that in such exper- ing (SM), only its T =0 component, only its T =1 component iments the challenge is to select the nucleus of interest, or no pairing at all (No np). Right: Schematic illustration of produced at a very low rate of about 300 atoms per hour, the structure of the ground state of 92Pd in the spin-aligned in the presence of a background of other reaction chan- proton-neutron paired phase. Figure adopted from Ref. [55]. nels which is about a million times higher. In this case the SHIP velocity filter, developed for the studies of superheavy elements (see section 4.1), has been used to sep- tors of the two proton holes align until the maximum spin arate the 190Po nuclei from the unwanted background be- + of 8 is reached. To examine the influence from differ- fore their implantation in a position-sensitive Si detector ent components of the proton-neutron interaction on the in which the subsequent α decay was detected. The ob- 92 excitation spectrum of Pd, additional shell model calcu- served fine structure of the α decay allowed for the iden- lations were performed including only the T =0 component tification of two excited 0+ states at energies of 532 and of the pairing, including only the T =1 part or finally ex- 650 keV as shown in Fig. 11. Based on additional ex- cluding proton-neutron pairing at all. As shown in Fig. 10, perimental information and the energy systematics in the in the latter case a seniority-type spectrum is obtained. heavier Pb isotopes (for a detailed discussion see Ref. [56]) For the full calculation (labeled SM in Fig. 10), the cal- it has been possible to assign spherical, oblate and prolate culated excitation energies agree very well with those de- shape to the three 0+ states at 0, 532, and 650 keV exci- duced from experiment. It is evident that the T =0 compo- tation energy, respectively. The unique feature of this case nent of the proton-neutron interaction plays an important of triple shape coexistence is that these three states are 92 role for the spectrum of Pd. This component can be visu- the lowest states at all in the energy spectrum of 186Pb. alized as spin-aligned (deuteron-like) proton-neutron hole On the theoretical side, the phenomenon of shape coex- 100 pairs with respect to the Sn core, spinning around the istence has been studied in the past using a number of centre of the nucleus (see Fig. 10). To conclude this sec- different approaches, among them microscopic shell model 92 tion, the structure of the heavy N=Z nucleus Pd differs descriptions and mean-field calculations (for an overview markedly from what has so far been observed in all known see Ref. [57]). An example of the latter, employing the atomic nuclei. In this exotic atomic nucleus strongly cou- Gogny force, is shown in Fig. 11 to illustrate the evolution pled proton-neutron pairs have a decisive influence on the of the potential energy surface for the A=182-192 Pb iso- structure of the nucleus. topes [58]. These calculations not only nicely describe the experimental excitation energies but furthermore provide explications for the existence of the three low-lying states 3.4 Shape coexistence in the lead isotopes of different shapes and of the evolution of these minima with the mass number. The observation that a particular atomic nucleus can exhibit eigenstates with different shapes appears to be a unique type of behavior in finite many-body quantum systems. States of different shapes are also known to exist in molecules. However, in that case they are based on geometrical arrangements of widely spaced atomic nuclei 12 Andrea Jungclaus: Single particle versus collectivity, shapes of exotic nuclei

show pronounced non-uniformities for certain magic proton and neutron numbers. Nuclei consisting of a magic number of protons or neutrons have increased binding energies relative to the average trend. The same effect is known from atoms (remember the increased stability of the nobel gases) and in analogy to atomic physics the nuclear shell model was developed. By the end of the 1960s, it had been concluded that these shell effects are the reason why atomic nuclei can be more stable than expected from the liquid drop model and therefore nuclei beyond Fermium can exist. Early calculations predicted the nucleus with Z=114 and N=184 to be the centre of an island of long-lived superheavy nuclei far beyond the limit of stability predicted by the liquid drop model [59–61]. This result stayed practically unchallenged until the late 1990s, when more refined models, based on realistic effec- tive nucleonnucleon interactions, were applied to superheavy nuclei. However, the microscopic models are still uncertain when extrapolating in Z and the mass number A leading to the fact that there is no consensus among theorists with regard to what should be the next doubly magic nucleus beyond 208Pb (Z=82, N=126) [62]. It is furthermore expected that superheavy elements can exist in a variety of shapes, including spherical, axial and triaxial configurations. As a consequence, besides the spherical shell closures mentioned above, also deformed shell gaps are anticipated. A sketch of the situation as predicted by theoretical calculations is shown in Fig. 12. On the experimental side, our present knowledge about the heavy mass end of the nuclear chart beyond the heaviest radioactive element existing in nature, Uranium with 92 protons, has been accumulated in three clearly separated phases during the last century. Following a sug- gestion by Enrico Fermi in 1934 (only two years after the discovery of the neutron by Chadwick!) the eight transura- nium elements from Neptunium (Z=93) up to Fermium (Z=100) have been synthesized by neutron capture and Fig. 11. Top: Scheme of the α decay of 190Po and partial level scheme of 186Pb. Bottom: Calculated potential energies for the Pb isotopes as function of the deformation. Figure adopted from Refs. [56,58]. spherical

4 The heavy end of the nuclear chart ? No 4.1 The synthesis of superheavy elements (SHE) Last known deformed Th,U Until the beginning of the 1950s it was not expected that elements beyond Fermium (Z=100) exist. At that time it last known was still assumed that an atomic nucleus consisting of nucleons can be regarded in analogy to a liquid drop built out of atoms. This liquid drop model allowed to describe many at that time modern phenomena like neutron-induced ﬁs- sion and neutron capture. In this model, it was expected Fig. 12. Sketch of the heavy end of the nuclear landscape. that around proton number 100 the repulsive Coulomb Besides the heaviest known doubly-magic nucleus 208Pb, theo- force would win over the attractive nuclear surface ten- retically predicted spherical and deformed shell gaps are indi- sion and the nuclei would decay spontaneously. As men- cated by white lines. The region around the predicted spherical tioned in the Introduction, only around 1950 it was re- doubly-magic nucleus 298114 is called island of stability. Be- alized that many nuclear properties are not smooth, uni- tween the main continent and this island of stability a region form functions of the proton and neutron numbers, but of deformed nuclear shapes is predicted. Andrea Jungclaus: Single particle versus collectivity, shapes of exotic nuclei 13

RIKEN 2004RIKEN 2004 σ ~fb = 10-39 cm2

1999 Hot fusion: More neutron-rich CN since Cold fusion: T1/2 long enough for chemistry ! Connected to known nuclei Dubna 2003 σ ~pb = 10-36 cm2 1996 GSI until

cold hot

Fig. 13. Summary of the current experimental knowledge of the upper end of the nuclear chart. The elements in the range Z=107-112 were discovered using cold fusion reactions at GSI, while the heavier elements up to element 118 were produced in hot fusion reactions at Dubna. Note that element 113 is the only SHE which was synthesized using both cold and hot fusion reactions (see text for details). The inset shows experimental cross sections for cold and hot fusion reactions as a function of the atomic number Z of the synthesized element. Figure adopted from Refs. [63,64]. successive beta-decay in the years 1940-1955. It is inter- fusion between a doubly-magic Pb target with heavy ions esting to remember that it was this idea by Fermi which of rather low energy below the Coulomb barrier leads to a lead to the discovery of the nuclear fission in 1938. How- much suppressed fission probability and therefore higher ever, this path to heavier nuclei stops at Fermium, since yields. In this so-called cold-fusion reaction, the excitation none of its isotopes decays via β decay due to the short α energy of the compound nucleus amounts to only about decay and fission half-lives. The elements with Z=101-106 10-20 MeV and already the evaporation of one (or two) were then produced between 1955 and 1974 by bombard- neutrons cools it down to a state stable against fission. ing the heaviest elements available, namely the transura- However, only in one out of thousand cases the compound nium elements produced in a high-flux reactor, with light nucleus gets rid of its excitation energy before fission oc- ions. The typical cross sections for such fusion-evaporation curs. Lead and Bismut are best suited as target material reactions are much smaller than the ones for neutron cap- because both spherical nuclei are stabilized by the Z=82 ture used for the lighter heavy elements making the ex- and N=126 shell closures. As beams neutron rich isotopes periments much more difficult. Note that at that time, close to shell closures are best. For the identification of the only the University of Berkeley in the US and the russian new very short-lived elements, a fast physical technique research center at Dubna were able to perform SHE re- has been applied instead of the slow chemistry. The trick search since only the nuclear weapon nations were in the is to separate the reaction products from the beam using possession of installations for the production of large sam- a velocity filter, to implant them into a Si detector and fi- ples of the heavy actinides, which were needed as target nally to identify them via their α decay. To synthesize the material. A reminder of this cold war period is the tough elements with Z=107-112 this correlation technique and fight about the names of the new elements with proton cold fusion reactions have been employed using the veloc- number Z=101-106. ity filter SHIP at GSI. An ion beam with a very high in- 12 With each new element, the production cross section tensity of about 3x10 ions/sec hits a target wheel which decreases by a factor of three or four (see inset of Fig. 13) rotates synchronously with the pulse structure of the beam and also the half-live drops drastically. It was therefore ev- in order to distribute the heat over a larger area. Nearly ident that in order to proceed to even heavier systems new all ions pass through the target without interaction. Only reactions as well as new identification methods had to be about once a week, a fusion product is produced, which searched for. Concerning the first, it had been realized that continues to move in the same direction as the beam ions, instead of bombarding heavy actinides with light ions, the however with a reduced velocity. The electric and mag- 14 Andrea Jungclaus: Single particle versus collectivity, shapes of exotic nuclei netic fields of the velocity filter SHIP are chosen such in this case. The second difference concerns the half-life that the fusion products hit a Si detector whereas the of the produced isotopes. Due to their larger neutron ex- ion beam is directed onto a beam catcher. In the position cess the isotopes produced in hot fusion reactions have sensitive Si detector, position, time and deposited energy longer half-lives which in some cases are even long enough of the implants are registered as well as time and energy to perform chemistry. There is one element, namely ele- of the subsequent α-decays. Using this technique elements ment 113, which has been synthesized both in cold and up to Z=112 could successfully be identified until 1996, hot fusion reactions. This case nicely illustrates the com- produced with cross sections as low as 10−36 cm2 (pb). plementary of the two techniques. At RIKEN the isotope 278113 was populated as one-neutron evaporation channel Around Z=112 the applicability of the cold fusion re- in the reaction 209Bi + 70Zn [65]. The cross section for this actions comes to an end. The main reason is that the cross reaction is extremely low, at the very limit of experimental section for the production of the evaporation residue de- feasibility, as evidenced by the fact that within 553 days creases exponentially with the increase of the proton num- with beam on target the decays of only three 278113 nuclei ber of the compound nucleus because of the increase of have been observed! Most important, in one of the events the Coulomb repulsion force. Note that when the com- a long chain of six α particles was observed which linked pound nucleus Z changes from 102 to 113, the cross sec- the new isotope to well-known and previously studied nu- tion drops by a factor of 108! Furthermore the evaporation clei. The half-life of this isotopes is very short, below one residue produced in cold fusion reactions are some 10-15 millisecond. In Dubna, on the other hand, the hot fusion mass units shifted from the β-stability line which leads to reaction 243Am + 48Ca was used to produce 288115 and as a considerable decrease in their half-lives further hinder- its α-decay daughter 284113, a more neutron-rich isotope ing its detection. At that point it was clear that one had of element 113, with much higher cross section [66]. How- to look for other reactions when aiming for the synthesis ever, in this case each of the isotopes in the decay chain of even heavier elements. In order to decrease the factors was new and had never been studied before. It is there- hindering fusion it was suggested that the use of neutron- fore necessary to study the chemical properties of the final rich isotopes of the actinides as targets and the doubly atom in the chain to prove that it was Dubnium (Z=105). magic nucleus 48Ca would be a good choice. For exam- The decision which of the two experiments, i.e. less am- ple, in the reaction 244Pu + 48Ca (Z ·Z = 1880), the P T biguity in the identification vs. larger number of events, Coulomb repulsion decreases by almost 40% as compared will be given preference when it comes to the assignment to the cold fusion reaction 208Pb + 76Ge (Z ·Z = 2624). P T of the naming rights is expected with great suspense. This drop is expected to reduce the factors hindering fusion in these reaction, which are called hot fusion reactions Considering all information about superheavy elements because the compound nucleus is produced at significantly available today, i.e. fission and α decay half-lives and de- higher excitation energies of 30 to 55 MeV leading to the cay modes, one remarkable observation is that nearly all evaporation of a larger number of neutrons as compared isotopes above Rutherfordium (Z=104) are α emitters. to cold fusion reactions. Another feature of these proposed That means that they are more stable against fission than hot fusion reactions is that they produce more neutron- the isotopes of Rutherfordium and Nobelium. Calculations rich compound nuclei. For example, the compound nucleus have shown that this stability comes from the ability of 292114, produced via the hot fusion reaction 244Pu + 48Ca, the nucleus to deform, with not only quadrupole but also has 8 neutrons more as compared to the one formed in higher multipole moments. Indeed, deformed shell gaps at the cold fusion reaction 208Pb + 76Ge reaction. Conse- neutron numbers N=152 and N=162 have been proposed quently, longer half-lives of the evaporation residue can (see Fig. 12) which in the first case have already been be expected. confirmed experimentally in recent mass measurements of No isotopes [67] and also by γ-ray spectroscopy as will be In 1999, the 244Pu+48Ca reaction was successfully used discussed in the next section. to synthesize the element 114 using the gas-filled recoil We close this section with the remark that the next separator DGFRS at the Joint Institute for Nuclear Re- heavier, so far undiscovered elements 119 and 120 have search (Dubna, Russia). This experiment opened a new already been searched for in a number of experiments per- era in SHE research which lead to the discovery of all el- formed at different laboratories in recent years. However, ements up to Z=118 using similar hot fusion reactions the results of these activities have not yet been presented. in the following years. The current experimental informa- For more detailed information about the exciting past and tion about SHE is summarized in Fig. 13. It was found presence of SHE research the reader is referred to Refs. [63, that the cross sections for hot fusion reactions are indeed 64] and references therein. relatively large, in fact all elements up to 118 can be produced in this way with a larger cross section as compared to the one of the cold fusion reaction used to synthesize element 112 (see inset of Fig. 13). Besides the cross section 4.2 The spectroscopy of transfermium nuclei there are two major differences between the production of SHE using cold and hot fusion reactions: First the iso- Nuclear spectroscopy is a very powerful tool to give access topes produced in hot fusion reactions do not decay into to nuclear structure and the properties at excitation en- the region of known isotopes (see Fig. 13). Therefore the ergies up to several MeV. Spectroscopic techniques can assignment must always be based on indirect arguments probe the single-particle states around the Fermi level Andrea Jungclaus: Single particle versus collectivity, shapes of exotic nuclei 15 and thus help to improve predictions of nuclear properties in nuclei not accessible for experimental studies today. Due to the very low production cross sections, until now it has not been possible to study SHE by means 254No of in-beam spectroscopic techniques. On the other hand, many of the transfermium nuclei (Z>100) are produced in fusion-evaporation reactions with cross-sections large enough, i.e. in the nb to µb range (see Fig. 13), to allow for their study using both in-beam and decay spectroscopy. Detailed spectroscopic studies of nuclei from Cm to Db allow to pin down the evolution of single-particle states in this region and provide valuable information on the details of the shell correction in heavy nuclei. Ultimately, such data can help to define the extent and location of the SHE island of stability. As discussed in the last section, the stability of the isotopes beyond Fermium is predicted to arise from nuclear deformation effects. The first direct proof of this prediction was presented by Reiter et al. in 1999, who observed a rotational band built on the ground state of 254 254No (Z=102) [68]. Excited states of this nucleus were No populated in the reaction 208Pb(48Ca,2n) with a cross section of 3 µb in an experiment performed at the Argonne National Laboratory (USA). The challenge was to identify γ rays emitted from excited states of 254No in a background of more than 10000-times more intense fission γ rays. This was accomplished by combining efficient γ-ray detection power with the ability of a residue separator to identify unambiguously very weekly produced evaporation residues. Prompt γ rays were detected using the Gamma- sphere spectrometer (see next section) positioned around the target wheel. The evaporation residues were separated from the beam by a fragment mass analyzer (FMA). At the focal plane of the FMA, the particles were detected in a position-sensitive Si detector. The production of 254No was unambiguously demonstrated by the observation of subsequent α decays at the same position in the Si detector where the implant has been detected. Both the α energies as well as the decay time correspond to the ones 254 known for the decay of 254No. The γ rays, which where de- Fig. 14. Top: γ-ray spectrum of No, showing the rotational 254 ground state band up to a spin of 24h ¯. Bottom: Level scheme tected in coincidence with the No residues, form a reg- 254 ular rotational band which in subsequent experiments was of No showing the rotational band on the left and three further extended up to spin 24+ [69] as shown in Fig. 14. excited structures including two isomeric states on the right. Adopted from Refs. [69,72]. Besides the first direct determination of the ground state deformation of a transfermium isotope, the observation of the rotational band up to spin 14+ in the pioneering relations [69]. Additional valuable information can be ob- work of Ref. [68] had another important implication. It tained from the study of excited states of non-collective demonstrated that neutron evaporation can compete up character. Since the nuclei in this region are deformed, the to at least this spin against fission. Hence, a fission bar- degenerate spherical single-particle orbitals split in a well rier must still exist up to this angular momentum - a fact, defined manner into components according to the projec- which is not at all obvious for a nucleus which exists only tion of the angular momentum onto the symmetry axis of due to shell effects. the nucleus as first described by Nilsson in 1955 [71]. Or- In the following years rotational bands were studied bitals which are relevant for the existence or not of spheri- in a number of additional even and odd nuclei in this re- cal shell gaps dive down and come close to the Fermi level gion, produced with cross sections as low as 17±3 nb in in lighter deformed nuclei and thus play a key role in the the case of 256Rf (Z=104) [70]. The systematic study of formation of excited states. In Ref. [72] three excited struc- rotational properties such as the kinematic and dynam- tures were identified in 254No (see Fig. 14), two of which ical moments of inertia revealed subtle effects believed with long half-lives in the µs and ms range, respectively. to be related to changes in alignment and pairing cor- Two of them correspond to configurations in which a pair 16 Andrea Jungclaus: Single particle versus collectivity, shapes of exotic nuclei of protons is broken and the two unpaired protons occupy different single-particle orbitals. The third most probably involves both a broken proton and a broken neutron pair. 158Er This new experimental data allowed the position of a particular Nilsson orbital to be determined, which is of special ) interest as the level originates from the spherical 2f5/2 orbital from above the possible spherical Z=114 shell gap. MeV / The separation and position of the 2f7/2 - 2f5/2 spin-orbit 2

partners plays a crucial role for predictions of the location (h of the island of stability. kin J An overview of recent in-beam and decay spectroscopy of transfermium nuclei is given in Ref. [69], for a more general glance the reader is referred to Ref. [73].

5 Atomic nuclei under extreme conditions Rotational frequency hω (MeV)

The study of the nucleus under extreme conditions with 158 respect to angular momentum and excitation energy played Er an important role in nuclear structure physics during the last decades. Deformed nuclei can rotate with high angu-

21 lar frequencies (of the order of 10 Hz for example for a ) mass A∼70 nucleus at spin 70¯h) which implies enormous

Coriolis forces. On the other hand, a nucleus can stand MeV ( around 5 MeV excitation energy, which corresponds to a x maximum temperature of about 5.8 x 1010 K. The nuclear E level density increases exponentially with the excitation energy which allows to apply a statistical treatment and the concept of nuclear temperature. The question to answer is how tens or even hundreds of strongly interacting nucleons react when they are exposed to the mentioned extreme conditions. Spin (h) In the first decades of experimental nuclear structure physics, experimental studies were limited to the investi- Fig. 15. Top: Kinematical moment of inertia as a function of gation of the properties close to the ground state. How- the rotational frequency for the yrast sequence of 158Er. The ever, in the same way as the availability of radioactive ion S-shape is usually referred to as a backbending and occurs due beams allowed during the last decades to study regions to the alignment of a pair of i13/2 neutrons. Below this crit- of the nuclear landscape further away from the valley of ical frequency value, the yrast sequence is composed of the 2 stability (see first part of this article), other technical ad- ground-state band, but after the backbend the i13/2 configura- vances, namely stable heavy ion beams and efficient γ-ray tion becomes yrast. Bottom: Excitation energy versus spin di- 158 spectrometer, facilitated the exploration of the excitation agram for the yrast sequence of Er. In this presentation the energy versus spin plane, i.e. the systematic study of the backbending appears as a crossing between two bands, namely the ground state band and the band built on an aligned i13/2 nuclear properties as a function of excitation energy (tem- + + perature) and angular momentum (rotational frequency). neutron pair, around spin 12 -14 . The origin of the so-called high spin physics dates back to the 1970s. While already in 1963 a regular rotational band, namely the ground state band of 160Dy, was ob- total spin) continues to increase. Choosing instead a pre- served for the first time up to the 10+ state [74], only in sentation in an excitation energy vs. spin diagram, the 1972 Johnson and collaborators discovered irregular spac- same irregularity shows up in form of a crossing between ings within this band in the spin range 14+-18+ [75]. In two rotational bands with different moments of inertia (see both experiments the α-induced fusion-evaporation reac- Fig. 15). The expressions backbending and band crossing tion 160Gd(α,4n)160Dy was employed but while in the first indeed describe the same phenomenon, namely the fact the emitted γ radiation was detected in a NaI scintillator, that at a certain rotational frequency, a configuration dif- in the second a Ge(Li) semiconductor detector was used ferent from the ground state configuration may become providing a much better energy resolution. Visualizing the energetically favoured. rotational band in a moment of inertia vs. rotational fre- Also in other nuclei in the rare earth region similar fea- quency diagram as it is shown in Fig. 15 the irregularity tures were observed [76]. Soon after the experiment, this appears as a backbending, the frequency of the collective observation has been interpreted by Stephens and Simon rotation decreases while the moment of inertia (and the as being due to the breaking of one pair of neutrons in the Andrea Jungclaus: Single particle versus collectivity, shapes of exotic nuclei 17

high-j intruder orbital i13/2 [77]. In contrast to this pic- constant spacing of 47 keV between neighbouring lines in- ture, Mottelson and Valatin predicted already in 1960s a dicates a very high moment of inertia corresponding to coherent collapse of pairing correlations at a certain crit- a strongly deformed shape of the nucleus. The existence ical rotational frequency, corresponding to a phase tran- of second minima in the nuclear potential corresponding sition from the superfluid to a non-superfluid state [78]. to very elongated or superdeformed shapes had been pre- The validation of the explanation by Stephens and Simon dicted since long time. The single-particle energies in a nu- came in 1977 from the observation of a second irregularity cleus depend on the shape of the potential. For spherical in the ground state rotational band of 158Er in the region shape, large energy gaps occur for the ”magic numbers” of around spin 32+, corresponding to a second pair of nucle- nucleons. However, adding more and more nucleons out- ons, this time protons in the h11/2 orbital [79]. Note that side closed shells leads to deviations from sphericity and only the availability of first heavy-ion accelerators at sev- energy gaps occur for different nucleon numbers at dif- eral laboratories in the 1970s allowed for the observation ferent deformations. The total energy which, neglecting of rotational bands up to spins as high as 32+, in the case residual interactions, is the sum of the single-particle en- of 158Er populated in the reaction 122Sn(40Ar,4n)158Er. ergies of all protons and neutrons in the nucleus under study, is a function of the deformation parameter and can have more than one minimum. Excited states in this sec- 5.1 Multi-detector γ-ray spectrometer and the discovery of superdeformation

The discovery of the backbending phenomenon in several rare earth nuclei and the systematic study of a number of rotational bands up to intermediate spin in other mass regions evidenced the importance of γγ coincidence information and consequently in the 1980s arrays consisting of 5 to 20 individual Ge detectors were put together replacing the two Ge(Li) detectors which have been the standard setup in γ-ray spectroscopy for many years. Around the same time first escape-suppression shields were introduced. In Ge, the cross-section for Compton scattering dominates for γ-ray energies above 180 keV and the probability that the Compton-scattered γ ray escapes from the Ge detector is high. Therefore, the peak-to-Compton ratio of the first Ge detectors was poor, with more than 90% of the interactions contributing to the Compton distribution and only less than 10% to the full-energy peak. The Compton continua of all the γ rays summed and made it difficult to detect a weak full-energy peak on the large Compton background created by the most intense γ rays. Surround- 152Dy ing the Ge crystal by a scintillator, initially in most cases NaI, the majority of the γ rays that are scattered out of the Ge detector are detected in this scintillator producing a veto signal which allows to reject the partly absorbed events before the γ-ray spectrum of the Ge detector is produced. In this way the background in this spectrum could be drastically reduced thus increasing the level of sensitivity. Based on this technical advancement the first discrete superdeformed (SD) rotational band has been observed by Twin et al. in 1986 in the nucleus 152Dy [80]. This nucleus was produced at high angular momentum at the Daresbury Laboratory (UK) using the heavy-ion induced fusion-evaporation reaction 108Pd(48Ca,4n)152Dy. The γ radiation emitted in the decay of the excited states of this Fig. 16. Top: γ-ray spectrum of the superdeformed band in nucleus was detected by the TESSA3 spectrometer which 152Dy discovered with the TESSA3 spectrometer at the Dares- consisted at the time of the experiment of twelve escape- bury laboratory. Note the nearly constant spacing of 47 keV suppressed Ge detectors. The efficiency of this instrument between two successive lines. Bottom: Non-collective states and was high enough to allow the observation of an extremely deformed bands in 152Dy in the excitation energy versus spin regular rotational band which collects only about 1% of plane. Some typical decay paths deexciting the superdeformed the total intensity of the main reaction channel 152Dy. The band to the oblate states are illustrated. Figure adopted from γ-ray spectrum of this band is shown in Fig. 16. The nearly Ref. [80]. 18 Andrea Jungclaus: Single particle versus collectivity, shapes of exotic nuclei ond minimum were first observed in an indirect way as of 110 individual Ge crystals while EUROBALL comprises resonances in the fission cross sections of nuclei in the ac- a total of 239, many of them mounted in composite de- tinide region in the 1960s. However, the direct observation tectors) both projects reached their goal and both instru- of the γ rays emitted in the decay of the superdeformed ments started operation in the 1990s. A detailed descrip- states only became possible with the increased sensitivity tion of these projects is presented in the review article of the γ-ray spectrometer available in the 1980s. As illus- by Eberth and Simpson [82]. The experiments performed trated in Fig. 16, at low excitation energy 152Dy has a with Gammasphere at the Argonne and Lawrence Berke- slightly oblate shape (β∼-0.1) and its yrast line is formed ley National Laboratories and EUROBALL at the LNL by irregularly spaced single-particle type excitations. At Legnaro (Italy) and the IReS Strasbourg (France) led to intermediate spin, a deformed rotational band is observed a tremendous gain in the knowledge of the nuclear struc- corresponding to a prolate deformation of about β∼0.1. It ture at high excitation energy and angular momentum. is only at very high angular momentum that the superdeformed band becomes energetically favoured because of As hoped for with the improved efficiency of these its large moment of inertia. One of the main questions new instruments the first discrete linking transitions which since the first observation of a superdeformed band was connect SD and normal yrast states in one step were fi- how such a SD band decays into the normal deformed or nally observed in the nucleus 194Hg in 1996. Note that at spherical minimum. The observation of this decay, which that time more than 100 SD bands in the mass 150 and is schematically indicated in Fig. 16, is hindered by several 190 regions had been found, but for none of these bands facts: At excitation energies of several MeV corresponding the exact excitation energies, spins and parity could be de- to the second minimum the density of states in the first termined. In the case of 194Hg [83], studied with Gammas- minimum is very high which leads to a fragmentation of phere at the LBNL employing the reaction 150Nd(48Ca,4n), the decay paths and as a consequence to low intensities of four high-energetic (3.5-4.5 MeV) electric dipole one-step the individual γ transitions which are furthermore of rel- linking transitions carrying about 5% of the SD band in- atively high energy so that the detection efficiency of the tensity have been observed and thereby energy and spin of Ge detectors is low. In addition the very different struc- the SD band fixed. The SD band is observed in the spin ture of the states in the two minima implies low transition range from 10¯h to 50¯h and at the bottom of the band, probabilities of the transitions between them. Considering furthermore the weak population of the superdeformed structures in fusion-evaporation reactions (because they are yrast only at very high spin) it is not surprising that it was not possible to observe the decay out of a superdeformed band with the first generation of γ-ray spectrometer such as TESSA or NORDBALL. Fortunately, the history of high-spin physics did not stop at this point. On the contrary, the discovery of superdeformation in 1986, which was considered as one of the major physics discoveries at that time [81], served as starting shot for the development of even larger and therefore more efficient 4π γ-ray spectrometer thus heralding a new era of the investigation of the behaviour of atomic nuclei at high excitation energy and angular momentum.

5.2 4π γ-ray spectrometer and the boom of high-spin physics

The first generation γ-ray spectrometer extended considerably the region of the excitation energy versus angular momentum plane accessible for experimental studies. For the first time, it became possible to study the behaviour of atomic nuclei at excitation energies up to 30 MeV and in the spin range up to 60¯h. In light of this GASP EUROBALL AGATA new perspective two large-scale projects were started at the end of the 1980s aiming for the construction of arrays Fig. 17. Overview of the sensitivities reached with different of escape-suppressed Ge detectors in 4π geometry with past and present γ-ray spectrometer. The state-of-the-art in- a photopeak efficiency of around 10%. To cope with the struments EUROBALL and Gammasphere, operational since cost of such arrays, large collaborations were formed aim- the mid-ninetees, allow to study excited states down to inten- ing for the construction of Gammasphere in the US and sities of about 10−6 of the production cross section. The next EUROBALL in Europe. Although using different techni- generation of 4π tracking arrays (AGATA, GRETA) will have cal approaches and geometries(e.g. Gammasphere consists even higher sensitivities. Andrea Jungclaus: Single particle versus collectivity, shapes of exotic nuclei 19 where the decay-out occurs, the SD states lie about 4.2 riety of mean field approaches. As example, we will briefly MeV above the ND yrast levels of the same spin. In 2002, discuss the superdeformed band in the N = Z nucleus sixteen years after its discovery, also the lowest SD band 60Zn, which represents the N = Z = 30 ”doubly magic” in 152Dy was connected to the remaining level scheme via superdeformed core in the mass 60 region. In contrast the observation of four weak γ transitions (schematically to for example the mass 150 region, in which the nuclei shown in Fig. 16) with intensities of together 1.7% of the of interest can be populated with large cross sections in intensity within the SD band [84]. In this case, the SD fusion-evaporation reactions but the intensity of the SD band is observed in the spin range 24+-62+. The present bands accounts for only about 1% of the channel, inter- understanding of the decay-out mechanism of SD bands estingly 60Zn is produced with only ∼0.1% of the total in the heavy mass regions is that it is a statistical pro- fusion cross section in the reaction 40Ca(28Si, 2α) at 125 cess governed by the weak mixing of SD states with one MeV but here the SD band is populated with about 60% or more of the adjacent closely spaced ”hot” levels in the of the channel intensity [86]. A superdeformed band con- normal well separated by a potential energy barrier. The sisting of eleven γ transitions in the energy range 1.1-3.7 decay than occurs through the admixed component of the MeV was observed. Two one-step linking transitions into normal deformed state in the SD state wave function. the ground state band as well as two additional two-step This statistical picture implies that the transition inten- cascades have been identified allowing for a firm energy sity fragments into so many weak branches that a direct and spin assignment of the SD band. There are two obser- identification of the linking transitions is possible only for vations which differ considerably from what we have seen the strongest ones. Still today, only for a few of the many in heavy nuclei. First, the identified linking transitions known superdeformed bands in the mass 150 and 190 re- account for a significant fraction (about 37%) of the SD gions excitation energies and spins are firmly assigned. intensity and second they are of stretched E2 character Much more systematic information is necessary in order instead of E1 as expected in a statistical decay process. to address such issues as (i) the magnitude of shell correc- Though a simple explanation for this observation is the tions at large deformation, (ii) the particle configuration suppression of isoscalar dipole transitions in N=Z nuclei, of the bands, (iii) the origin of identical SD bands and the fact that the discrete decay-out scheme of the yrast (iv) the mechanisms responsible for the sudden decay-out SD band in the N=Z+1 nucleus 59Cu is also dominated of the SD bands. by stretched E2 transitions indicates that this is not the full truth. Although still most of the decay-out intensity is After the first pioneering experiments in very heavy fragmented over a large number of weak multistep path- nuclei, superdeformation has been shown to be a widespread ways, some of the observed linkings have E2 transition phenomenon across the nuclidic chart. Besides the A=150 strengths of up to 2 W.u., which is much too large to and A=190 mass regions discussed above, strongly de- be explained within a purely statistical decay-out model formed rotational bands in the second minimum have been used in the heavier mass regimes. Of course, the differ- observed since then in many other nuclei around A∼130, ent level densities may play an important role, although A∼80, A∼60 and more recently also in the A∼40 re- the phase space, i.e. the excitation energy of the superde- gion. In the twenty years after the discovery of superdeformed states in the region of the decay-out, is comparable formation in 1986 more than 250 discrete SD bands all for the A∼60 and the A∼190 regions. An additional ex- over the chart of nuclides were identified. In addition, planation for the seemingly selective decay-out pattern in several excited superdeformed rotational bands were ob- the mass 60 region arises from the fact that the configu- served through the study of the quasi-continuum part of rations of superdeformed and spherical states differ only the γ-ray spectra [85]. In-beam studies of light to medium by a relatively small number of nucleons while in heavier mass N∼Z nuclei are more challenging due to (i) the large nuclei SD and ND configurations differ by the rearrange- number of different residual nuclei produced in the reac- ment of a substantial number of nucleon pairs. This fact tions (up to some 30), (ii) relatively large γ-ray energies hints at the inclusion of pairing in an appropriate decay- and therefore low detection efficiencies and (iii) consid- out model. More theoretical effort is certainly needed in erable Doppler broadening caused by the relatively high order to understand the decay-out mechanism in this mass velocities and the large angle spread of the recoils induced region and relate it to the patterns observed in other mass by charged-particle emission. Only the powerful combina- regions. tion of highly efficient 4π Ge detector arrays and ancillary detector systems, especially charged particle and neutron The probably most spectacular result of the studies detectors, enabled the great progress in this field. Inter- in the A∼60 region has been the discovery of the unique estingly, superdeformation shows different aspects in the new decay mode of prompt discrete-energy proton and different mass regions. The N=Z nuclei around doubly- α decays from high-spin states located in the strongly magic 56Ni and 40Ca are of special interest for the follow- or superdeformed minimum of the nuclear potential into ing reasons: (i) spherical and superdeformed magic num- daughter states of spherical shapes. The particle decays bers appear at similar particle numbers leading to dra- compete with the conventional γ decay-out. The first case matic examples of shape coexistence and (ii) these nuclei in which such a decay-out via charged particle emission are amenable to different theoretical treatments that in- has been observed was 58Cu populated in the reaction clude shell model calculations in large configuration spaces, 28Si(36Ar,αpn)58Cu [87]. As illustrated in Fig. 18 a strongly quantum Monte Carlo shell model descriptions and a va- deformed band (β2∼0.37) has been observed in this nu- 20 Andrea Jungclaus: Single particle versus collectivity, shapes of exotic nuclei

58 57 proton spectra the binding energy difference between Cu and Ni as well as the transition energies of the observed γ rays. A 58 closer inspection reveals that only about 3% of the de- Cu29 excitation of the 8915 keV states proceeds via γ decay, whereas proton emission accounts for the remaining 97%. Since the discovery of this new mode of prompt discrete proton decay from excited states in the second minimum several other cases have been observed in neighbouring nuclei, among them also the doubly-magic nucleus 56Ni [88]. Furthermore, soon after the first proton decay in 58Cu, also a first case of prompt α decay has been identified, 58 57 namely from a deformed band in Ni into the spherical Ni29 6+ yrast daughter state in 54Fe [89]. In subsequent experiments the level scheme of 58Ni was then significantly extended including now at least 14 discrete particle decays, protons and α particles, into excited states of the daughter nuclei 57Co and 54Fe [90]. The discussed particle decays are two-dimensional quantum tunneling processes, in the course of which the remaining nuclear mean field is rearranged dramatically. Quantum-mechanical tunneling is a wide-spread phenomenon in the natural sciences. Therefore, a full understanding of this process may be of importance far beyond nuclear physics. In the last paragraph we already mentioned, quite in- cidentally, that proton emission from a deformed rotational band was also observed in the doubly-magic nucleus 56Ni. Even two well-deformed rotational bands have been identified in this nucleus, one of them decaying via proton emission to the ground state of 55Co [88]. Large- scale shell model calculations have shown to be able to Fig. 18. Illustration of the discovery of prompt discrete proton emission from an excited state in the second minimum of 58Cu. simultaneously describe the spherical excited states and The proton and γ-ray energy spectra prove the existence of two the first rotational band within the pf shell, the rota- parallel decay branches out of the deformed minimum, via γ tional band being built upon a four-particle four-hole (4p- decay to the spherical minimum of 58Cu on one hand side and 4h) excitation. This example nicely illustrates that even via proton emission to a spherical excited state in the isotone a doubly-magic nucleus can assume a deformed shape at 57Ni on the other. Figure adopted from Ref. [87]. not too high excitation energy and that furthermore these deformed structures can be described in the frame of the spherical shell model. cleus consisting of seven stretched quadrupole transitions An even more impressive example for shape coexis- (purple in Fig. 18). This band is linked to the spherical tence in a doubly-magic nucleus is the lighter self-conjugate part of the level scheme via a 4.171 MeV γ transition (pink nucleus 40Ca. This is a very special case for the simple rea- in Fig. 18). This is the expected behaviour. The surprise son that for particle number 20 energy gaps are predicted is that requesting a coincidence with the lowest member to exist not only for spherical shape, but also for different of the deformed band, namely the γ ray with 830 keV, be- prolate and oblate deformations. In the single-particle di- sides the in-band transitions some γ rays known to belong agram shown in Fig. 19, in addition to the spherical gap, to the isotone 57Ni are observed (green in Fig. 18). These two prolate and one oblate deformed shell gaps are present data indicate that the 8915 keV band head of the strongly at β2 values around -0.4, 0.3, and 0.6, respectively. Two deformed band in 58Cu decays predominantly via proton rotational bands, built on the first two excited 0+ states, emission into the spherical 3701 keV level in the daugh- were indeed observed in this nucleus by Ideguchi and co- ter nucleus 57Ni. This conclusion was confirmed through workers, who populated the excited states of this nucleus a careful examination of the proton energy spectra. In co- using the reaction 28Si(20Ne,2α)40Ca [91]. A partial ex- incidence with γ rays emitted from excited states in the perimental level scheme of 40Ca is shown in Fig. 19. In first minimum, the protons show a broad energy distri- order to determine the deformation of these bands tran- bution characteristic of protons evaporated in the fusion- sition quadrupole moments were deduced from the mea- evaporation reaction (remember that 58Cu was populated sured fractional Doppler shifts of all in-band transitions as αpn reaction channel). In contrast, in coincidence with as a function of the γ-ray energy. Assuming a rigid axi- the 830 keV transition connecting excited states in the de- ally symmetric rotor these measured quadrupole moments formed second minimum, a sharp peak at 2.4(1) MeV is correspond to quadrupole deformations of β2∼0.27 for the observed. This is the energy expected taking into account band built on the first excited 0+ state (blue in Fig. 19) Andrea Jungclaus: Single particle versus collectivity, shapes of exotic nuclei 21

Exp. SM β2=0.6(1) proportional to 8p-8h ~0.27 transition strength 40 β2 4p-4h Ca20

β2 + 03 + 02

β2~0 + A. Poves 01

Fig. 19. Comparison between the experimentally established (left) and calculated (right) excitation scheme (partial) of the doubly-magic nucleus 40Ca (taken from Refs. [91,92]). See text for details.

and β2=0.6(1), i.e. superdeformed shape, for that on top atomic nucleus at high excitation energy and high angu- of the second excited 0+ level (red in Fig. 19). In Ref. [91] lar momentum. Heavy-ion induced fusion-evaporation re- the features of the two bands were explained by cranked actions were shown to be an efficient tool to populate nu- relativistic mean field calculations to arise from 4p-4h re- clei at spins as high as 70¯h and excitation energies up to spectively 8p-8h excitations. 35 MeV. The sensitivity of the experiment then mainly Recently, an attempt was made to describe the dra- depends on the efficiency of the γ-ray spectrometer used matic example of shape coexistence observed in 40Ca within to detect the long cascades of γ rays emitted in the de- the spherical shell model considering a valence space con- excitation of these states towards the ground state. How sisting of two major shells, namely the pf and the sd shell, closely the progress in the exploration of the Ex vs. I plane and allowing for the creation of up to eight particle-hole is related to the advancement in instrumentation becomes pairs, i.e. excitations of nucleons from the sd to the pf evident when considering the case of 158Er (see Ref. [93] shell [92]. The result of this calculation is compared to for details). As mentioned in Section 5, this nucleus was the experimental excitation scheme in Fig. 19. As can be one of the first cases in which Coriolis-induced pair break- seen not only the excitation energies, but also the transi- ing (backbending) was discovered in 1972 [76] and the first tion strengths within the two rotational bands are nicely in which a second alignment was observed [79]. The first reproduced by the shell model calculations. As in the case alignment of two i13/2 neutrons at spin ∼14¯h and the sec- of the mean field calculations mentioned above also the ond alignment of two h11/2 protons at spin ∼28¯h were SM assigns 4p-4h respectively 8p-8h character to the nor- illustrated already in Fig. 15 and are shown in Fig. 20 mal deformed and superdeformed bands built on the ex- again, this time in the Ex vs. I plane. In the 1980s the cited 0+ states. This example illustrates in an impressive TESSA and HERA arrays of Ge detectors enabled the way that with the exploration of the excitation energy observation of a dramatic change of structure around spin versus spin plane, a field which was initiated in the 1970s 38¯h. Less collective band structures, which reach high spin with the discovery of the backbending phenomenon, the by aligning the single-particle angular momenta of the va- 146 thinking in fixed categories, e.g. the shell model is used lence nucleons outside the Gd82 core, become energet- to describe spherical nuclei close to the shell closures and ically favoured. The alignment of the valence particles in the collective models are used to describe excitations of these bands causes the shape of the nucleus to become deformed nuclei in the open shells, had to be abandoned. oblate. These bands are called terminating bands because they terminate once all valence particles are aligned to the maximum available spin, in the case of 158Er in the range 46-49¯h. This case can actually be considered a textbook 5.3 The future of γ-ray spectroscopy example of the phenomenon of band termination in heavy nuclei. However, the story of 158Er does not stop here. To In the last section we tried to give an idea about the generate even higher angular momentum the 146Gd core richness of phenomena which were observed studying the 22 Andrea Jungclaus: Single particle versus collectivity, shapes of exotic nuclei

always be covered by collimators to prevent the radiation from the target to directly enter the compton-suppression (CS) shields. This problem of solid angle covered by dead material is illustrated in Fig. 21 which shows the view from the target position into one half of the EUROBALL spectrometer. The only way to overcome this hindrance is the use of a Ge shell, i.e. an instrument consisting ex- clusively of Ge crystals. Monte Carlo simulations show that in this way photopeak efficiencies of 40-60% can be reached. However, the problem of the Ge shell is to dis- tinguish between two γ rays emitted from the target and detected in two adjacent detectors and one γ ray emitted from the target and Compton scattered from one to the other detector. The only solution to this problem is to increase the number of Ge detectors in the shell to 1000 or more in order to reduce the probability that two co- incident γ rays from a high multiplicity cascade interact with neighbouring detectors. Unfortunately, such a solution is unrealistic due to its extremely high cost. A new perspective then opened up with the development of the Fig. 20. Evolution of the nuclear structure of 158Er with spin. first segmented Ge detectors in the beginning of this cen- Excitation energies of a variety of observed structures are plot- tury. Position-sensitivity of the detectors is achieved by ted with respect to a rigid-rotor reference in order to emphasize the changes that occur along and close to the yrast line. The both segmentation of the outer contact and by analyzing strongest new high moment-of-inertia band is included, but the charge drift times within a segment and the mirror its exact excitation energy is not known. The inset illustrates charges induced in the neighbouring segments. Using dig- the changing shape of 158Er with increasing spin within the ital electronics and pulse-shape analysis techniques it is standard (,γ) deformation plane (from Ref. [93]). possible to identify the energy, time and position of every interaction point of a γ ray as it interacts, scatters and is finally absorbed in the 4π ball. The full event can be reconstructed offline using algorithms based on the Klein- has to be broken which costs about 1 MeV of energy at Nishina formula. 50¯h. Some weak high-energy γ rays decaying from states This is the new concept in array design, based on γ-ray beyond band termination into the band-terminating states tracking in highly segmented germanium detectors (see have been observed in 2006 using the Gammasphere γ-ray Fig. 21). Besides the increase in efficiency there is another spectrometer [94]. The so far last chapter in the saga of aspect which makes γ-ray tracking arrays very attractive. 158Er was written shortly after with the identification of The reconstruction of the position of the first interaction four rotational structures, displaying high moments of in- point in the segmented Ge crystal allows for a very pre- ertia, which extend up to spin 65¯h and bypass the band- cise determination of the angle of γ emission relative to terminating states discussed above. These bands imply the the beam axis. As a consequence, a much better Doppler return of collective rotation at ultrahigh spin. Comparison correction can be achieved as compared to the use of un- with cranked Nilsson-Strutinsky calculations suggests that these sequences are most likely strongly deformed triaxial structures. It is an amazing feature that the nucleus 158Er exhibits a variety of different shapes in different regions of Compton Shielded Ge EUROBALL • scattered -rays lost the Ex vs. I plane, from prolate to oblate and further to εph ~ 10% γ • poor definition of Ndet ~ 100 triaxial deformation, and all this during the few picosec- angle of incidence onds between the population of the highly excited nucleus Ω ~ 40% • solid angle coverage until it reaches its ground state. Note that the strongly de- Δθ ~ 8º limited by CS shields formed bands carry only about 10−5-10−4 of the channel Ge Tracking Array Combination of: intensity. With the observation of these bands the sensi- • segmented detectors ~ 50% tivity limit of instruments such as Gammasphere and EU- εph • digital electronics Ndet ~ 100 • pulse shape analysis ROBALL is reached (compare Fig. 17). To proceed and to • γ-ray tracking fully explore the spin regime until fission sets in, the de- Ω ~ 80% much improved efficiency Δθ ~ 1º and angle definition AGATA velopment of new, even more powerful γ-ray spectrometer is necessary. Fig. 21. Comparison between conventional 4π γ-ray spec- Using γ-ray spectrometer built out of escape-supressed trometer consisting of unsegmented Ge crystals such as EU- Ge detectors the photopeak efficiency is limited to about ROBALL and the future tracking arrays such as AGATA. The 10% (the efficiency reached with Gammasphere and EU- use of segmented Ge detectors in combination with digital elec- ROBALL) due to the simple fact that independent on the tronics, pulse shape analysis and tracking algorithms leads to exact geometry a large fraction of the total solid angle will a much improved efficiency and sensitivity. Andrea Jungclaus: Single particle versus collectivity, shapes of exotic nuclei 23 segmented detectors whenever the γ rays are emitted from and triaxiality, new decay modes such as prompt charged a moving nucleus. This is particularly important for γ-ray particle emission from excited states in the second min- spectroscopy using fast radioactive ion beams. The con- imum as well as the study of shape coexistence, phase cept of a tracking arrays was first tested and successfully transitions and new modes of collective excitations such demonstrated by smaller arrays of segmented detectors as the wobbling mode [100]. such as the SeGA array at NSCL [95], the MINIBALL at ISOLDE [96] or the TIGRESS array at TRIUMF (Van- couver, Canada) [97]. The field of nuclear physics research has undoubtedly Using highly segmented Ge crystals a 4π Ge shell can experienced a renaissance during recent years and all the be realized which consists of only 100-200 instead of the exciting results stimulate appetite for more. Currently, 1000 individual detectors needed in the case of unseg- the next generation of high intensity radioactive beam mented crystals as mentioned above. Monte Carlo sim- facilities using both in-flight and ISOL techniques is in ulations show that with this reduced number of crystals the planning stage both in the US and in Europe (FAIR, (and consequently reduced cost) such an array would still FRIBS, EURISOL etc.). These facilities will provide ra- be able to combine a very high photopeak efficiency (max- dioactive ion beams over a wide energy range and with in- imum coverage of the solid angle with Ge detectors) with tensities much higher than available at the moment. This an excellent ability to correct for Doppler effects and a will not only allow to establish the limits of nuclear exis- very good peak-to-total ratio (by distinguishing between tence for heavier elements up to Manganese (Z=25) but fully and partially absorbed events). As in the late 1980s, the higher intensities for neutron-rich nuclei will enable when the Gammasphere and EUROBALL projects were in addition the measurement of basic properties such as launched in parallel by American and European collabora- masses and lifetimes which are crucial e.g. for our under- tions, respectively, two projects aiming for the construc- standing of astrophysical processes. For many isotopes the tion of 4π tracking arrays are currently under way. The available intensities will be high enough to perform sec- American project is called GRETA (Gamma Ray Energy ondary reactions with the radioactive beams, e.g. fusion- Tracking Array) and in Europe scientists from twelve dif- evaporation reactions or transfer reactions. Looking at the ferent countries are working on the AGATA (Advanced proton-rich side of the nuclear chart, it will for the first GAmma Tracking Array) project. Although the design of time be possible to map the proton drip line for medium- the two instruments is basically very similar, in detail dif- mass odd-Z nuclei and to identify ground state proton ferent technical solutions are chosen. For a detailed discus- emitters up to Z=93. Concerning the heaviest nuclei, the sion of the technical aspects of these projects see Ref. [98, synthesis of new species may become possible in the fu- 99]. sion of re-accelerated neutron-rich radioactive beams with 208Pb, 238U or 248Cm targets. The exploration of these neutron-rich superheavy nuclei furthermore would help 6 Outlook to put the identification of SHE created in hot fusion- evaporation reactions with stable beams on a solid footing. In this article I have discussed some recent achievements in the field of nuclear structure physics. I tried to demon- Of course, parallel to the development of more intense strate that within the last few decades, the limits of our radioactive beam facilities the current instrumentation has knowledge of the atomic nucleus have been pushed out to be improved. One example is the development of an tremendously in two different directions. First, it became improved fragment separator “Super-FRS” at GSI, an- feasible to study nuclei far-off stability at the limits of nu- other one new γ-ray spectrometer for the use at radioac- clear binding, i.e. in the regions of extreme isospin and tive beam facilities. Even though radioactive beams from extreme masses. These studies lead to the discovery of the next generation facilities will often approach today’s surprising phenomena such as neutron halos and skins on intensity of stable beams, the most exotic nuclei under the neutron-rich side as well as the first observation of investigation will always be produced with extremely low two-proton radioactivity and spectroscopic studies behind rates. A γ-ray spectrometer to study these nuclei must be the proton dripline on the proton-rich side. In particular, a universal instrument that fulfills some strict criteria. The the study of light neutron rich nuclei taught us that part best solution seems to be a 4π shell of large segmented Ge of our established knowledge about the atomic nucleus, crystals in which the individual interaction points of the gained over many years studying nuclei close to the valley γ quanta are disentangled numerically in order to allow of stability, may have to be revised in regions far-off sta- for an efficient Doppler correction. Both in the US and bility. In particular, the concept of a static shell structure Europe such tracking arrays are currently under develop- with global magic numbers all over the chart of nuclei had ment. to be given up in favor of a more dynamic view of shell evolution, in which classical magic numbers can disappear in certain regions of nuclei while new shell gaps can arise. In conclusion, everything is prepared for a very excit- On the other hand, atomic nuclei have been investigated ing future of nuclear physics research and we are looking under exotic conditions such as very high temperature or forward to many more surprises the atomic nucleus is cer- high rotational frequency. These studies enabled the dis- tainly still keeping for us. covery of exotic shapes in nuclei, e.g. superdeformation 24 Andrea Jungclaus: Single particle versus collectivity, shapes of exotic nuclei

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